The Hellmann–Feynman theorem for approximate wave functions and its application to nonadiabatic coupling matrix elements with the aid of a coupled Hartree–Fock method

1980 ◽  
Vol 72 (10) ◽  
pp. 5532-5539 ◽  
Author(s):  
Peter Habitz ◽  
Christian Votava
Keyword(s):  
Wave Functions ◽  
Matrix Elements ◽  
Coupling Matrix ◽  
Nonadiabatic Coupling ◽  
Hartree Fock ◽  
Approximate Wave ◽  
Feynman Theorem

On the evaluation of nonadiabatic coupling matrix elements using SA‐MCSCF/CI wave functions and analytic gradient methods. I

1984 ◽  
Vol 81 (10) ◽  
pp. 4549-4553 ◽  
Author(s):  
Byron H. Lengsfield ◽  
Paul Saxe ◽  
David R. Yarkony
Keyword(s):  
Gradient Methods ◽  
Wave Functions ◽  
Matrix Elements ◽  
Coupling Matrix ◽  
Nonadiabatic Coupling

Inelastic Scattering of High Energy Electrons by Helium

1973 ◽  
Vol 51 (3) ◽  
pp. 311-315 ◽  
Author(s):  
S. P. Ojha ◽  
P. Tiwari ◽  
D. K. Rai
Keyword(s):  
Ground State ◽  
High Energy ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Final States ◽  
Interaction Type ◽  
Hartree Fock ◽  
High Energy Electrons ◽  
Approximate Wave ◽  
Accurate Wave

Generalized oscillator strengths and the cross section for excitation of helium by electron impact have been calculated in the Born approximation. Transitions from the ground state to the n1P (n = 2 and 3) states have been considered. Highly accurate wave functions of the Hartree–Fock and "configuration–interaction" type have been used to represent the ground state. Approximate wave functions due to Messmer have been employed for the final states. The results are compared with other calculations and with experiment.

Ab initio study of nonadiabatic coupling matrix elements between excited 22A′ and 32A′ electronic states of C2H

2001 ◽  
Vol 336 (1-2) ◽  
pp. 135-142 ◽  
Author(s):  
Alexander M. Mebel ◽  
Michael Baer ◽  
Victor M. Rozenbaum ◽  
Sheng H. Lin
Keyword(s):  
Ab Initio ◽  
Electronic States ◽  
Matrix Elements ◽  
Ab Initio Study ◽  
Coupling Matrix ◽  
Nonadiabatic Coupling

Brillouin's theorem and the Hellmann-Feynman theorem for Hartree-Fock wave functions

1971 ◽  
Vol 20 (4) ◽  
pp. 687-694 ◽  
Author(s):  
C.A. Coulson
Keyword(s):  
Wave Functions ◽  
Hartree Fock ◽  
Feynman Theorem

Zur Theorie der Auger-Prozesse in III — V-Halbleitern

1969 ◽  
Vol 24 (11) ◽  
pp. 1752-1759
Author(s):  
Dieter Schöne
Keyword(s):  
Transition Probability ◽  
Wave Functions ◽  
Matrix Elements ◽  
Bloch Functions ◽  
Radiative Transitions ◽  
Excess Electrons ◽  
Approximate Wave ◽  
Auger Effect

Abstract This paper presents a calculation of the lifetimes of excess electrons in the III -V compounds InSb, InAs and GaSb, assuming the Auger effect between bands. Following the theory of Beattie and Landsberg matrix elements are calculated by using approximate wave functions instead of Bloch functions. The ninefold integration of the transition probability can be reduced to a four-fold one which then is numerically calculated with the aid of a computer. The results are compared with the lifetimes of radiative transitions. It is shown that the Auger processes are dominant in small gap semiconductors, but not in semiconductors with larger gaps (more than about 0.5 eV).

scholarly journals Nonadiabatic Dynamics Algorithms with Only Potential Energies and Gradients: Curvature-Driven Coherent Switching with Decay of Mixing and Curvature-Driven Trajectory Surface Hopping

2021 ◽  
Author(s):  
Yinan Shu ◽  
Linyao Zhang ◽  
Shaozeng Sun ◽  
Yudong Huang ◽  
Donald Truhlar ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Wave Functions ◽  
Matrix Elements ◽  
Nonadiabatic Dynamics ◽  
Time Step ◽  
Coupling Matrix ◽  
Surface Hopping ◽  
New Methods ◽  
Electronic Structure Methods ◽  
Curvature Driven

Direct dynamics by mixed quantum–classical nonadiabatic methods is an important tool for understanding processes involving multiple electronic states. Very often, the computational bottleneck of such direct simulation comes from electronic structure theory. For example, at every time step of a trajectory, nonadiabatic dynamics requires potential energy surfaces, their gradients, and the matrix elements coupling the surfaces. The need for the couplings can be alleviated by employing the time derivatives of the wave functions, which can be evaluated from overlaps of electronic wave functions at successive timesteps. However, evaluation of overlap integrals is still expensive for large systems. In addition, for electronic structure methods for which the wave functions or the coupling matrix elements are not available, nonadiabatic dynamics algorithms become inapplicable. In this work, building on recent work by Baeck and An, we propose new nonadiabatic dynamics algorithms that only require adiabatic potential energies and their gradients. The new methods are named curvature- driven coherent switching with decay of mixing (κCSDM) and curvature-driven trajectory surface hopping (κTSH). We show how powerful these new methods are in terms of computer time and good agreement with methods employing nonadiabatic coupling vectors computed in conventional ways. The lowering of the computational cost will allow longer nonadiabatic trajectories and greater ensemble averaging to be affordable, and the ability to calculate the dynamics without electronic structure coupling matrix elements extends the dynamics capability to new classes of electronic structure methods.

Potential curves and nonadiabatic coupling matrix elements for the O+−Ne system

2009 ◽  
Vol 16 (S13) ◽  
pp. 475-484
Author(s):  
Ole Halkjaer ◽  
Jan Linderberg
Keyword(s):  
Matrix Elements ◽  
Coupling Matrix ◽  
Nonadiabatic Coupling ◽  
Potential Curves
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